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The hydrodynamic force on a rigid particle undergoing arbitrary time-dependent motion at small Reynolds number

Lovalenti, Phillip M. and Brady, John F. (1993) The hydrodynamic force on a rigid particle undergoing arbitrary time-dependent motion at small Reynolds number. Journal of Fluid Mechanics, 256 . pp. 561-605. ISSN 0022-1120. http://resolver.caltech.edu/CaltechAUTHORS:LOVjfm93a

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Abstract

The hydrodynamic force acting on a rigid spherical particle translating with arbitrary time-dependent motion in a time-dependent flowing fluid is calculated to O(Re) for small but finite values of the Reynolds number, Re, based on the particle's slip velocity relative to the uniform flow. The corresponding expression for an arbitrarily shaped rigid particle is evaluated for the case when the timescale of variation of the particle's slip velocity is much greater than the diffusive scale, a^2/v, where a is the characteristic particle dimension and v is the kinematic viscosity of the fluid. It is found that the expression for the hydrodynamic force is not simply an additive combination of the results from unsteady Stokes flow and steady Oseen flow and that the temporal decay to steady state for small but finite Re is always faster than the t^-½ behaviour of unsteady Stokes flow. For example, when the particle accelerates from rest the temporal approach to steady state scales as t^-2.


Item Type:Article
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http://dx.doi.org/10.1017/S0022112093002885PublisherUNSPECIFIED
Additional Information:Copyright © 1993 Cambridge University Press. Reprinted with permission. (Received 5 August 1992 and in revised form 27 May 1993) P.M.L. wishes to thank Rockwell International for providing financial support as a Rockwell Fellow during the course of this study. The authors also gratefully acknowledge H.A. Stone for many helpful discussions and insightful comments in the preparation of this article.
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Deposited On:21 Oct 2008 06:24
Last Modified:26 Dec 2012 10:26

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